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arXiv · 2212.05508

Noetherian $π$-bases and Telgársky's Conjecture

Servet Soyarslan·Süleyman Önal
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Abstract

We investigate Noetherian families and show that every topological space has a Noetherian $π$-base. We prove that if a topological space has some special Noetherian $π$-bases, then NONEMPTY has a 2-tactic in the Banach-Mazur game on a space $X$, denoted as $BM(X)$, whenever NONEMPTY has a winning strategy in BM(X). This result encompasses an important theorem of Galvin in this context and is related to Telgársky's conjecture on this subject. One of our examples is that any space $X$ with $πw(X)\leq ω_1$ has this special Noetherian $π$-base. We pose some questions about this topic.

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Servet Soyarslan, Süleyman Önal. 2025-01-25. Noetherian $π$-bases and Telgársky's Conjecture. https://arxiv.org/abs/2212.05508

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